It is likely to lead to a tightening up of rules allowing schools to select pupils along religious lines, although the details are yet to be finalised.

The Lib Dems have previously called for faith schools to admit more pupils from families that refuse to support their religious ethos, as well as an end to rules that allow them to opt out of equalities legislation.

In an interview this year, Mr Cameron said: “I think that faith schools are a really important part of our education system and they often have a culture and ethos which helps to drive up standards. If anything, I would like to see faith schools grow.”

A document published on Thursday – outlining the principles of the coalition’s legislative programme – confirmed plans to allow new providers to open new schools funded by the taxpayer.

In a controversial move, any parents’ group, company, charity or teachers’ organisation will be able to run their own “free school “to meet local demand.

It is understood that more religious groups will be encouraged to run more schools under this system. Faith schools currently make up a third of all state schools in England.

The coalition agreement also said schools would have more flexibility to alter the curriculum and run their own qualifications.

It would give schools the power to offer courses such the International GCSE, which is currently banned in the state sector, despite being favoured in private schools.

The document also outlines plans to:

Provide a “pupil premium” – extra money for schools educating children from the poorest backgrounds – funded by cuts from outside the schools’ budget

Review Sats tests for primary school pupils

Allow schools to pay higher salaries to good teachers, reforming the existing “rigid” national pay rules

Introduce incentives to attract top science and mathematics graduates into teaching

Create a new wave of technical schools that allow 14- to 19-year-olds to learn a trade alongside the basics of English, maths and science.

In the universities and skills sectors, the coalition pledged to abolish many of the quangos running further education. Extra money will be used to create more apprenticeships, internships and college places.

The government also said it would await the outcome of an independent review into tuition fees led by Lord Browne, the former head of BP.

The Lib Dems – which oppose a rise in fees – will be allowed to abstain from any Commons vote on the issue.